The 1990 Seminar on Stochastic Processes was held at the University of British Columbia from May 10 through May 12, 1990. This was the tenth in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, the Univer sity of Florida, the University of Virginia and the University of California, San Diego. Following the successful format of previous years, there were five invited lectures, delivered by M. Marcus, M. Vor, D. Nualart, M. Freidlin and L. C. G. Rogers, with the remainder of the time being devoted to informal communications and workshops on current work and problems. The enthusiasm and interest of the participants created a lively and stimulating atmosphere for the seminar. A sample of the research discussed there is contained in this volume. The 1990 Seminar was made possible by the support of the Natural Sciences and Engin~ring Research Council of Canada, the Southwest University Mathematics Society of British Columbia, and the University of British Columbia. To these entities and the organizers of this year's conference, Ed Perkins and John Walsh, we extend oul' thanks. Finally, we acknowledge the support and assistance of the staff at Birkhauser Boston.

The 1991 Seminar on Stochastic Processes was held at the University of California, Los Angeles, from March 23 through March 25, 1991. This was the eleventh in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, the University of Florida, the University of Virginia, the University of California, San Diego, and the University of British Columbia. Following the successful format of previous years there were five invited lectures. These were given by M. Barlow, G. Lawler, P. March, D. Stroock, M. Talagrand. The enthusiasm and interest of the participants created a lively and stimulating atmosphere for the seminar. Some of the topics discussed are represented by the articles in this volume. P. J. Fitzsimmons T. M. Liggett S. C. Port Los Angeles, 1991 In Memory of Steven Orey M. CRANSTON The mathematical community has lost a cherished colleague with the passing of Steven Orey. This unique and thoughtful man has left those who knew him with many pleasant memories. He has also left us with important contributions in the development of the theory of Markov processes. As a friend and former student, I wish to take this chance to recall to those who know and introduce to those who do not a portion of his lifework.

The 1992 Seminar on Stochastic Processes was held at the Univer sity of Washington from March 26 to March 28, 1992. This was the twelfth in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, University of Florida, University of Virginia, University of California, San Diego, University of British Columbia and University of California, Los An geles. Following the successful format of previous years, there were five invited lectures, delivered by R. Adler, R. Banuelos, J. Pitman, S. J. Taylor and R. Williams, with the remainder of the time being devoted to informal communications and workshops on current work and problems. The enthusiasm and interest of the participants cre ated a lively and stimulating atmosphere for the seminar. A sample of the research discussed there is contained in this volume. The 1992 Seminar was made possible through the support of the National Science Foundation, the National Security Agency, the Institute of Mathematical Statistics and the University of Washing ton. We extend our thanks to them and to the publisher Birkhauser Boston for their support and encouragement. Richard F. Bass Krzysztof Burdzy Seattle, 1992 SUPERPROCESS LOCAL AND INTERSECTION LOCAL TIMES AND THEIR CORRESPONDING PARTICLE PICTURES Robert J.

This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.

During the of Fall 1991, The Centre de Recerca Matematica, a research institute sponsored by the Institut d'Estudis Catalans, devoted a quarter to the study of stochastic analysis. Prominent workers in this field visited the Center from all over the world for periods ranging from a few days to several weeks. To take advantage of the presence in Barcelona of so many special ists in stochastic analysis, we organized a workshop on the subject in Sant Feliu de Guixols (Girona) that provided an opportunity for them to ex change information and ideas about their current work. Topics discussed included: Analysis on the Wiener space, Anticipating Stochastic Calculus and its Applications, Correlation Inequalities, Stochastic Flows, Reflected Semimartingales, and others. This volume contains a refereed selection of contributions from some of the participants in this workshop. We are deeply indebted to the authors of the articles for these exposi tions of their valuable research contributions. We also would like to thank all the referees for their helpful advice in making the volume a reflection of the dynamic interchange that characterized the workshop. The success of the Seminar was due essentially to the enthusiasm and stimulating discus sions of all the participants in an informal and pleasant atmosphere. To all of them our warm gratitude.

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.